Supersymmetric 4D Orientifolds of Type IIA with D6-branes at Angles

TL;DR

This work constructs four-dimensional $\mathcal{N}=1$ Type IIA orientifolds using $\Omega\mathcal{R}$ with D6-branes at non-trivial angles, focusing on $\mathbb{Z}_3$, $\mathbb{Z}_4$, $\mathbb{Z}_6$, and $\mathbb{Z}_6'$ toroidal orbifolds. By computing Klein bottle, annulus, and Möbius strip amplitudes and enforcing a complete tree-channel projector, the authors obtain tadpole-free solutions and determine closed- and open-string spectra; all analyzed models yield non-chiral massless spectra, with gauge-group ranks reduced by powers of two as predicted by prior arguments. For $\mathbb{Z}_4$ and $\mathbb{Z}_6$ cases, some open-string spectra arrange into $\mathcal{N}=2$ multiplets accidentally, while the underlying setups remain $\mathcal{N}=1$; the multiplicities of twisted open-string sectors are given a geometric interpretation as invariant intersection points. The results illuminate how lattice orientation choices generate inequivalent models and point to avenues for non-supersymmetric generalizations and dual descriptions, contributing to the broader landscape of perturbatively consistent 4D string vacua.

Abstract

We study a certain class of four-dimensional N=1 supersymmetric orientifolds for which the world-sheet parity transformation is combined with a complex conjugation in the compact directions. We investigate in detail the orientifolds of the Z_3, Z_4, Z_6 and Z_6' toroidal orbifolds finding solutions to the tadpole cancellation conditions for all models. Generically, all the massless spectra turn out to be non-chiral.

Figures (6)

• Figure 1: The $\mathbb{Z}_4$ lattices
• Figure 2: Branes on the $\mathbb{Z}_4$ torus
• Figure 3: Branes on the $\mathbb{Z}_3$ torus
• Figure 4: The $\mathbb{Z}_6$ lattices
• Figure 5: Branes on the $\mathbb{Z}_6$ torus